SPDEs driven by space-time white noise in high dimensions: absolute continuity of the law and convergence of solutions |
| |
Authors: | TS Zhang WA Zheng |
| |
Institution: | 1. Department of Mathematics , University of Manchester , Oxford Road, Manchester MPL, 13 9, England, UK;2. Department of Mathematics , University of California at Irvine , 92697, Irvine, CA, USA |
| |
Abstract: | In this paper, we consider stochastic partial differential equations driven by space-time white noise in high dimensions. We prove, under reasonable conditions, that the law of the solution admits a density with respect to Lebesgue measure. The stability of the equation, as the higher order differential operator tends to zero, is also studied in the paper. |
| |
Keywords: | Malliavin Calculus Stochastic partial differential equations Semigroups Eigenvalues and Eigenvectors 60H07 60H15 60G20 60G60 |
|
|